 995 P.K. Mitter, B.Scoppola
 Renormalization group approach to
interacting polymerised manifolds
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Jan 7, 99

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Abstract. We propose to study the infrared behaviour of
polymerised (or tethered) random manifolds of
dimension $D$ interacting via an exclusion condition
with a fixed impurity in $d$dimensional Euclidean
space in which the manifold is embedded. In this paper
we take $D=1$, but modify the underlying free Gaussian
covariance (thereby changing the canonical
scaling dimension of the Gaussian random field) so as
to simulate a polymerised manifold with fractional dimension
$D:\ 1<D<2$. We prove rigorously, via methods of Wilson's
renormalization group, the convergence to a non Gaussian fixed point
for $\e>0$, sufficiently small. Here, $\epsilon=1\beta{d\over 2}$, where
$\beta/2$ is the canonical scaling dimension of the Gaussian embedding
field. Although $\epsilon$ is small, our analysis is nonperturbative
in $\epsilon$. A similar model was studied earlier [CM] in the
hierarchical approximation.
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